High NA Fibers

Our last two posts have concerned the efficiency of coupling light into fibers. We've been asked whether we can use a fiber with a higher numerical aperture to improve this efficiency. In principle, the answer is yes. If we used a fiber with a numerical aperture of 0.50, accepting rays up to 30 degrees from the optical axis, we'd capture approximately twice as many rays as a fiber of the same size with NA=0.37. However, we've been unable to source fibers that both have such large acceptance cones and meet our project's other requirements.

We are currently Optran Ultra fibers which have a silica core, silica cladding, and a polyimide coating. Their numerical aperture is 0.37. The polyimide coating serves no optical purpose and is burned off in the tapering process, leaving an all-glass fiber.

There are 0.48 NA fibers available from Thorlabs (such as PN: BFL48-400), which are constructed of a silica core, polymer cladding, and Tefzel buffer. One such fiber has a 400μm core and 430μm cladding, but the Tefzel buffer is 730μm in diameter. We cannot taper these fibers without destroying the polymer cladding. We could simply polish the end of the fiber and insert it into the brain, but the blunt end would cause more tissue damage than a tapered fiber. Another problem arises with the Tefzel buffer. It is thick, making the fiber's cross sectional area 2.75 times larger than a fiber with the same core size and a 440μm total diameter (as is available in 0.37NA). We expect this greater size may be more invasive. We could attempt to strip the Tefzel coating off of the fiber, but Thorlabs warns against this:

The cladding material utilized to achieve the large NA of these fibers is a softer polymer than normally found in polymer clad step-index multimode fibers. Consequently, the cladding material has a higher probability of being removed from the fiber when the buffer is being stripped for normal connectorization.

There are other high NA fibers on the market. The Optran Ultra line includes fibers with numerical apertures greater than 0.37, but these fibers also rely optically on a polymer cladding. Their construction consists of a glass core, glass cladding, polymer buffer, and Tefzel jacket. According to a company representative whom we spoke with, the the polymer buffer is optically active. These fibers are, effectively, double step index fibers. We anticipate the same difficulty stripping them as we would encounter with the Thorlabs fiber. Like the Thorlabs fiber, the thick Tefzel coating increases the total size without increasing the light-gathering surface area. For example, the NA= 0.53 fiber has a core diameter of 200μm has a total diameter of 500μm (compared with our current use of 300μm core, 330μm total). In this case, the high NA fiber would only have 44% the light gathering surface of our current fiber, but over 2 times the total cross sectional area - making it more intrusive for similar power delivery.

Dennis Kaetzel has pointed us to "page 30 in the doric catalogue attached for 300um / 0.48NA and 200um / 0.53NA". We are investigating this fiber. If its construction is all-glass, unlike that sold by Thorlabs and CeramOptec, we ought to be able to achieve great capture efficiency and make tapers out of it. Otherwise, the difficulties discussed above remain.

According to Shibata et al. in "High Numerical Aperture Multicomponent Glass Fiber", a glass made of 40% PbO by weight will have refractive index 1.65 as compared to usual glass with index 1.55. Using the lead glass as a core we could obtain a numerical aperture of 0.56. In practice, they obtained 0.50. This would give us an acceptance cone of +-34 deg. Compared to our existing +-22 deg, we would get double the capture efficiency. It may be that all-glass fibers like this are not commercially available. Perhaps in the future we could custom order this kind of fiber. In the meantime, we can continue to refine our tapering and production process. The construction techniques we develop ought to carry over easily to any all-glass fiber that we find in the future.

There is an alternate way to use polymer-cladded fibers. We have equipped our tapering machine with an oxy-hydrogen micro torch as the heater. It produces a very small hot-zone. When we turn the flame on, it heats a length of fiber under 1mm long to glowing hot. This is the region of the fiber that is tapered (we produce gradual tapers by translating the hot zone along the length of the fiber). We begin tapering fibers with the polyimide still intact and it is burned off by the heat. The polyimide coating burns back approximately 2mm from behind the hot zone. Supposing that we were able to successfully strip the Tefzel coating off of a high NA fiber without damaging the polymer cladding, we could taper it and accept that the polymer coating will be damaged. We don't know how the polymer coating withstands heat, but it might be possible that is not damaged much more than polyimide. In this case, we could have a sharp, short taper (1mm long) at the tip of the fiber that minimizes damage to neural tissue upon insertion. Immediately behind the taper would be a 2mm zone of bare glass where the polymer cladding will have been burned off.

Illustration: A 0.48NA optical fiber with one end tapered. The polymer cladding is removed for 2mm behind the tapered region due to the heat of the tapering process.

Where exactly the light is emitted from the fiber using this approach would depend heavily on the optical properties of the brain. If its refractive index is uniformly similar to water, the brain may act as cladding and most light would not exit the fiber until the tapered region. If, however, there are a sufficient number of particles of high refractive index which interact with the fiber, the majority of light may be pulled out of the 2mm long section without cladding. In that case, it may be impossible to concentrate light output into as small of a volume as is possible with our current approach.

To this point, our work has been focused on all-glass fibers, so we will continue working with all-glass, NA=0.37 fiber, and plan on experimenting with other approaches as we perfect the tapering and production process. We will readily experiment with high NA fiber made of all glass if we can find it.

LED-Fiber Coupling

We have developed a system of coupling optic fibers to LEDs. We use a bare Cree C460EZ500 die that has been bonded to a surface mount chip and has had its cathode wire bonded to one of the chip's pads. The die's light emitting surface is exposed to air so that an optical fiber can be lowered directly onto it. We mount this chip onto a simple PCB and screw the PCB onto a three-dimensional micrometer stage. The optic fiber is held by a clamp while the stage manipulates the PCB, raising the die to the fiber. We use a digital microscope to monitor this progress.

Image: EZ-500 bare die (white) bonded onto a surface mount chip. The die measures 480x480μm, while the chip measures 3.25x3.25mm. Wire-bonded anode and cathode wires are visible connecting to the chip's pads.

We used our stage to abut several kinds of optical fiber to the LED, one at a time, to test the coupling efficiency (the amount of light captured by the fiber, divided by the die's total output). For fibers with cross sectional area smaller than the area of the die, this simple abutment of fiber end to the die is the most efficient method of coupling light into the fiber, as discussed by Hudson, 1974. We abut one end of a 15cm length of fiber to the die. We then measure the coupling efficiency by measuring the light output at the distal end of the optic fiber and dividing this by the total optical power of the LED. We measured the coupling efficiency of four different fibers to range from 0.12% to 17% (for {62.5micron core, NA = .22} and {400micron core, NA=.37}, respectively).

Images: Above, a fiber with a 300μm core, 360μm total diameter. The fiber is not centered over the die, but is instead adjacent to the gold bond pad. Below, a fiber with 62.5μm core (125 μm total) is centered over the die. Click for larger version.

We summarize the coupling efficiency of four different fibers in the table below. The measurements were taken with 72.1mA passing through the EZ-500. Total output was measured to be 56.3mW. We will provide a discussion of these results in our next post.

Image: Light being coupled into a 300μm core fiber.

References:
M. Hudson, "Calculation of the Maximum Optical Coupling Efficiency into Multimode Optical Waveguides," Appl. Opt.  13, 1029-1033 (1974).

Theoretical Capture Efficiency

The intensity of light emitted by an LED is greatest in the direction perpendicular to its surface. The EZ290 data sheet shows the irradiance of the LED varying approximately as the cosine of the angle from the normal to the LED surface. If we place a fiber with numerical aperture a above the LED, so that it is perpendicular to the LED surface, and the fiber is large enough that all the light emitted by the LED enters the core of the fiber, we see that light within an angle φ = arcsin(a) of the fiber axis will propagate by total internal reflection down the length of the fiber. The following calculation shows how the fraction of the LED power output propagating down the fiber will vary with φ

We have fibers with numerical aperture 0.37, for which we obtain φ = 22°. Of the light entering the core of such a fiber from the LED, we expect only 14% to propagate down the fiber. If the fiber is too small in diameter to cover the entire LED surface we expect our capture efficiency will be even lower.